International stock portfolio selection and performance measures recognizing higher moments of return distributions

Since the seminal works of Markowitz (1952), Sharpe (1964), and Lintner (1965), numerous studies on portfolio selection and performance measure have been based upon the mean-variance framework. However, several researchers (e.g., Arditti (1967, and 1971), Samuelson (1970), and Rubinstein (1973)) argue that the higher moments cannot be neglected unless there is reason to believe that: (i) the asset returns are normally distributed and the investor's utility function is quadratic, or (ii) the empirical evidence demonstrates that higher moments are irrelevant to the investor's decision. Based on the same argument, this dissertation investigates the impact of higher moments of return distributions on three issues concerning the 14 international stock markets.^ First, the portfolio selection with skewness is determined using: the Polynomial Goal Programming in which investor preferences for skewness can be incorporated. The empirical findings suggest that the return distributions of international stock markets are not normally distributed, and that the incorporation of skewness into an investor's portfolio decision causes a major change in the construction of his optimal portfolio. The evidence also indicates that an investor will trade expected return of the portfolio for skewness. Moreover, when short sales are allowed, investors are better off as they attain higher expected return and skewness simultaneously.^ Second, the performance of international stock markets are evaluated using two types of performance measures: (i) the two-moment performance measures of Sharpe (1966), and Treynor (1965), and (ii) the higher-moment performance measures of Prakash and Bear (1986), and Stephens and Proffitt (1991). The empirical evidence indicates that higher moments of return distributions are significant and relevant to the investor's decision. Thus, the higher moment performance measures should be more appropriate to evaluate the performances of international stock markets. The evidence also indicates that various measures provide a vastly different performance ranking of the markets, albeit in the same direction.^ Finally, the inter-temporal stability of the international stock markets is investigated using the Parhizgari and Prakash (1989) algorithm for the Sen and Puri (1968) test which accounts for non-normality of return distributions. The empirical finding indicates that there is strong evidence to support the stability in international stock market movements. However, when the Anderson test which assumes normality of return distributions is employed, the stability in the correlation structure is rejected. This suggests that the non-normality of the return distribution is an important factor that cannot be ignored in the investigation of inter-temporal stability of international stock markets. ^

Space time coding for polynomial phase modulated signals

Polynomial phase modulated (PPM) signals have been shown to provide improved error rate performance with respect to conventional modulation formats under additive white Gaussian noise and fading channels in single-input single-output (SISO) communication systems. In this dissertation, systems with two and four transmit antennas using PPM signals were presented. In both cases we employed full-rate space-time block codes in order to take advantage of the multipath channel. For two transmit antennas, we used the orthogonal space-time block code (OSTBC) proposed by Alamouti and performed symbol-wise decoding by estimating the phase coefficients of the PPM signal using three different methods: maximum-likelihood (ML), sub-optimal ML (S-ML) and the high-order ambiguity function (HAF). In the case of four transmit antennas, we used the full-rate quasi-OSTBC (QOSTBC) proposed by Jafarkhani. However, in order to ensure the best error rate performance, PPM signals were selected such as to maximize the QOSTBC’s minimum coding gain distance (CGD). Since this method does not always provide a unique solution, an additional criterion known as maximum channel interference coefficient (CIC) was proposed. Through Monte Carlo simulations it was shown that by using QOSTBCs along with the properly selected PPM constellations based on the CGD and CIC criteria, full diversity in flat fading channels and thus, low BER at high signal-to-noise ratios (SNR) can be ensured. Lastly, the performance of symbol-wise decoding for QOSTBCs was evaluated. In this case a quasi zero-forcing method was used to decouple the received signal and it was shown that although this technique reduces the decoding complexity of the system, there is a penalty to be paid in terms of error rate performance at high SNRs.

On-screen pre-deblurring of digital images using the wavefront aberration function of the human eye to improve computer access for the visually impaired

Traditional Optics has provided ways to compensate some common visual limitations (up to second order visual impairments) through spectacles or contact lenses. Recent developments in wavefront science make it possible to obtain an accurate model of the Point Spread Function (PSF) of the human eye. Through what is known as the "Wavefront Aberration Function" of the human eye, exact knowledge of the optical aberration of the human eye is possible, allowing a mathematical model of the PSF to be obtained. This model could be used to pre-compensate (inverse-filter) the images displayed on computer screens in order to counter the distortion in the user's eye. This project takes advantage of the fact that the wavefront aberration function, commonly expressed as a Zernike polynomial, can be generated from the ophthalmic prescription used to fit spectacles to a person. This allows the pre-compensation, or onscreen deblurring, to be done for various visual impairments, up to second order (commonly known as myopia, hyperopia, or astigmatism). The technique proposed towards that goal and results obtained using a lens, for which the PSF is known, that is introduced into the visual path of subjects without visual impairment will be presented. In addition to substituting the effect of spectacles or contact lenses in correcting the loworder visual limitations of the viewer, the significance of this approach is that it has the potential to address higher-order abnormalities in the eye, currently not correctable by simple means.